Module $(\varphi,\psi)$-amenability of Banach algebras

Bodaghi, Abasalt

Archivum mathematicum, Tome 46 (2010) no. 4, pp. 227-235.

Résumé

Let $S$ be an inverse semigroup with the set of idempotents $E$ and $S/\approx$ be an appropriate group homomorphic image of $S$. In this paper we find a one-to-one correspondence between two cohomology groups of the group algebra $\ell ^1(S)$ and the semigroup algebra $ {\ell ^{1}}(S/\approx )$ with coefficients in the same space. As a consequence, we prove that $S$ is amenable if and only if $S/\approx $ is amenable. This could be considered as the same result of Duncan and Namioka [5] with another method which asserts that the inverse semigroup $S$ is amenable if and only if the group homomorphic image $S/\sim $ is amenable, where $\sim $ is a congruence relation on $S$.

Détail

Classification : 43A07, 46H25
Keywords: Banach modules; module derivation; module amenability; inverse semigroup